1. Field of the Invention
The present invention relates to a peak to average power ratio (PAPR) reduction method and, more particularly, to a peak to average power ratio (PAPR) reduction method using bit reallocation, adapted for fields including a multi-carrier system or an orthogonal frequency division multiplexing (OFDM) system and the like.
2. Description of Related Art
In recent years, because a multi-carrier system, such as an OFDM system, can overcome multi-path interference and also increase spectral efficiency without using complicated transmitters and receivers, it is widely applied in many communication systems such as ADSL, DAB, DVB, WLAN (IEEE 802.11a, HiperLAN/2), WMAN (IEEE 802.16a) and the like.
A bit loading technique is typically used to increase the capacity of a multi-carrier system. Namely, after power allocation for transmissions at different sub-carriers (sub-channels) is determined, the transmissible information (i.e., the number of bits) and a mechanism of corresponding signal constellations at different sub-carriers are determined. FIG. 1 is a graph illustrating a typical Water-filling technique used for power allocation to achieve channel capacity and best spectral efficiency in a frequency selective channel. As shown in FIG. 1, for an AWGN channel, its frequency response is constant at all sub-carriers. Thus, information carried at each sub-carrier is allocated with same power to achieve channel capacity. However, for a multi-path frequency selective fading channel or any time varying channel, the channel capacity may not be achieved by the cited constant power allocation. Accordingly, a Water-filling technique is applied for transmissions over these channels.
As shown in FIG. 1, the frequency response of a frequency selective channel is divided into N frequency segments. The frequency response of each segment can be regarded to be constant for a multi-carrier system. Furthermore, in a multi-carrier system, one sub-carrier carries information over one frequency segment. If the frequency response is h1, h2, . . . , hN respectively at the N sub-carriers and the power spectrum density (PSD) of noise is σ12, σ22, . . . σN2 respectively in the N sub-carriers, the channel signal to noise ratio (CNR) can be defined as:
            γ      i        =                                                  h            i                                    2                    σ        i        2              ,      i    =    1    ,  2  ,  ⋯  ⁢          ,      N    .  
For a
  1      γ    i  to frequency graph as shown in FIG. 1, assumed that water is injected into along the curve, the amount of water at the peak of the curve is less than that at the valleys. At this point, the amount of water represents the transmission power Pi at each sub-carrier to be allocated.
After power allocation for transmissions at all sub-carriers is determined, a bit loading technique is applied to determine the transmissible number of bits at different sub-carriers. FIG. 2 shows a schematic diagram of functional blocks of a transmitting end in which an adaptive bit loading technique is applied. In FIG. 2, the transmitting end includes an adaptive constellation mapping unit 11, an adaptive bit loading unit 12, a serial to parallel (S/P) unit 13, an inverse fast Fourier transform (IFFT) unit 14, and a parallel to serial (P/S) unit 15. As shown in FIG. 2, the number of bits carried at different sub-carriers can be adjusted in dynamic against a time varying channel. Let B be the system transmission bandwidth, Δf be the frequency difference between any two adjacent sub-carriers and N be the number of sub-carriers, thusB=N*Δf.
The total transmission power P for the system can be computed by the equation of:
      P    =                  ∑                  i          =          1                N            ⁢                          ⁢              P        i              ,where Pi is the transmission power at the i-th sub-carrier and 1≦i≦N. In addition, the total number of bits R per signal block transmitted by the system with transmission bandwidth B is:
      R    =                  ∑                  i          =          1                N            ⁢                          ⁢              R        i              ,where Ri is the number of bits per signal block carried by the i-th sub-carrier. Given conditions upon channel features (channel frequency response and frequency spectrum density of noise), power allocation, modulated signaling (such as QAM, the Quadrature Amplitude Modulation), bit error rate (BER) requirement, and power margin, the maximum number of bits Ri per signal block transmissible by the i-th sub-carrier can be computed by the well-known equation [ref] of:
            R      i        =                  log        2            ⁡              (                  1          +                                                    P                i                            ⁢                              γ                i                                                                    γ                m                            ⁢                              γ                b                                                    )              ,where γm is the power margin for overcoming abrupt attenuation or additional noise appearing at the sub-carriers of a time varying channel and γb is the “SNR gap” in the well-known “gap approximation” [ref]. For example, γb=9 dB if a theoretical limit bit error rate ε=10−7.
To maximize the total number of transmission bits, D, of one signal block in a multi-carrier system without violating the system constraint of maximal transmission power Pmax, the mathematical expressions are given below:
                    max        ⁢                  {                                                    ∑                0                                  N                  -                  1                                            ⁢                                                          ⁢                              d                i                                      =            D                    }                                        subject        ⁢                                  ⁢        to        ⁢                                  ⁢                              {                                                            ∑                  0                                      N                    -                    1                                                  ⁢                                                                  ⁢                                  P                  i                                            ≤                              P                max                                      }                    .                    
As cited, Campello's first bit loading algorithm could be applied in the prior art to achieve the purpose. Let Pi(di) represent the transmission power allocated at the i-th sub-carrier with di bits, Δd represent the number of bit increment of one adjustment (for example, in the Campello's first algorithm, Δd=1) for bit loading, and ΔPi(di) represent the power increment required for increasing the number of transmission bits from (di−Δd) to di. Then, ΔPi(di) can be represented by the following equation,
      Δ    ⁢                  ⁢                  P        i            ⁡              (                  d          i                )              =      {                                                                      P                i                            ⁡                              (                                  d                  i                                )                                      -                                          P                i                            ⁡                              (                                                      d                    i                                    -                                      Δ                    ⁢                                                                                  ⁢                    d                                                  )                                                              if                                                    d              i                        ≥                          Δ              ⁢                                                          ⁢              d                                                                                                      P                i                            ⁡                              (                                  d                  i                                )                                      -                                          P                i                            ⁡                              (                0                )                                                              if                                                    d              i                        <                          Δ              ⁢                                                          ⁢                              d                .                                                        
The cited bit allocation at each sub-carrier is not adjusted until both the following conditions are met:
                                          Condition            ⁢                                                  ⁢            1            ⁢                          :                        ⁢                                                  ⁢            Δ            ⁢                                                  ⁢                                          P                i                            ⁡                              (                                  d                  i                                )                                              <                      Δ            ⁢                                                  ⁢                                          P                j                            ⁡                              (                                                      d                    j                                    +                                      Δ                    ⁢                                                                                  ⁢                    d                                                  )                                                    ,                  ∀          i                ,                  j          ∈                      {                          1              ,              2              ,              ⋯              ⁢                                                          ,              N                        }                          ,        and                                          Condition          ⁢                                          ⁢          2          ⁢                      :                    ⁢                                          ⁢          0                ≤                              P            max                    -                                    ∑                              i                =                1                            N                        ⁢                                          P                i                            ⁡                              (                                  d                  i                                )                                                    <                              min            j                    ⁢                      Δ            ⁢                                                  ⁢                                                            P                  j                                ⁡                                  (                                                            d                      j                                        +                                          Δ                      ⁢                                                                                          ⁢                      d                                                        )                                            .                                          
In fact, the aforementioned purpose can also be achieved by means of any bit loading algorithm in a multi-carrier system.
However, a high peak to average power ratio (PAPR) possibly occurs not only before applying any bit loading algorithm but also after doing that. An OFDM system or a multi-carrier system with high PAPR usually incurs incremental complexity and reduced efficiency on the application of an analog-to-digital converter (ADC), digital-to-analog converter (DAC), power amplifier (PA) or line driver (LD).
Therefore, it is desirable to provide an improved PAPR reduction method to mitigate and/or obviate the aforementioned problems.